6th IARP -TC-15 Workshop on Graphbased Representations in Pattern Recognition

Learning with spectral representations and use of MDL principles

author:Edwin Hancock, University of York
published: July 19, 2007, recorded: June 2007, views: 180

Slides

Slides
0:00	Recent Progress on Learning with Graph Representations
0:26	Outline
1:27	Motivation
1:29	Problem
2:04	Problem (2)
2:22	Problem (3)
2:43	Measuring similarity of graphs
4:49	Viewed from the perspective of learning
5:34	Learning with graphs (circa 2000)
9:34	Why is structural learning difficult
11:34	Structural Variations
12:32	Contributions
13:39	Spectral Methods
14:43	Graph (structural) representations of shape
15:06	Delaunay Graph
15:43	MOVI Sequence
15:53	Shock graphs
16:42	Graph characteristics
17:39	Pairwise clustering
17:49	Embeddings
17:51	Generative model
18:26	Spectral Generative Model
18:27	Algebraic graph theory (PAMI 2005)
18:53	….joint work with Richard Wilson
18:57	Spectral Representation
20:47	Properties of the Laplacian
21:35	Eigenvalue spectrum
22:00	Eigenvalues are invariant to permutations of the Laplacian.
22:35	Why
23:08	Symmetric polynomials
23:53	Power symmetric polynomials
24:08	Symmetric polynomials on spectral matrix
24:17	Spectral Feature Vector
25:10	…extend to weighted attributed graphs.
25:27	Complex Representation
26:42	Spectral analysis
27:15	Pattern Spaces
27:35	Manifold learning methods
27:38	Separation under structural error
27:40	Variation under structural error (MDS)
28:20	CMU Sequence
28:34	MOVI Sequence
28:36	YORK Sequence
28:44	Visualisation (LLP+Laplacian Polynomials)
29:21	Cospectrality problem for trees
30:35	Cospectral trees
30:54	Overcome using quantum random walk
31:42	The positive support of a matrix
32:05	Cospectral Trees
33:00	Stongly regular graphs
33:51	Generative Tree Union Model
34:11	..work with Andrea Torsello
34:18	Ingredients
34:21	Illustration
35:37	Cluster structure
35:40	Model
35:42	Union as tree distribution
35:44	Generative Model
35:58	Max-likelihood parameters
36:04	Description length
36:05	Expectation on observation density
36:06	Tree Union
36:28	Description length
37:18	Tree Union
38:13	Simplified Description Cost
38:16	Description Length Gain
38:44	Unattributed
39:57	Future

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